Except. He's wrong.ThomasMorgan wrote:
Winner.Aries_37 wrote:
The 64 = 65 paradox arises from the fact that the edges of the four pieces, which lie along the diagonal of the formed rectangle, do not coincide exactly in direction. This diagonal is not a straight segment line but a small lozenge (diamond-shaped figure), whose acute angle is
arctan 2/3 - arctan 3/8 = arctan 1/46
which is less than 1 degree 15' . Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can easily prove that the area of the "hidden" lozenge is equal to that of a small square of the chessboard.
Goodbye
EDIT:we did this back in high school it's so basic o.O
pictures ahere http://mathworld.wolfram.com/DissectionFallacy.html
There is not a lozenge as Aries_37 describes, though this is the usual way in which the puzzle is presented. Rather, if you look carefully at the large diagonal in the second figure, you will see that it is not a single line - it's three line segments:
Last edited by Scorpion0x17 (2008-03-19 21:15:19)